1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Electric field at the center of a semicircle

  1. Apr 1, 2013 #1
    1. The problem statement, all variables and given/known data

    See the image attached

    2. Relevant equations
    Ex = (Kλ/R)*∫3/2ππ/2(cosθ)dθ


    3. The attempt at a solution

    Ey cancels because there is an equal amount of force in both y directions. For the electric field on the x axis, the above equation can be used.

    Given that λ=Q/L

    λ=(85x10^-9 C)/(0.1 m)
    =8.5x10^-7

    R = L/θ
    =(0.1 m)/(3/2π - π/2)
    =0.03183

    E = ((8.85x10^-9)(8.5x10^-7)/0.03183)*pi
    = 7.424640507894822×10^-13

    This is not correct. Please help! Thanks in advance.
     

    Attached Files:

  2. jcsd
  3. Apr 1, 2013 #2
    take an element dx at θ with width dθ
    then integrate from 0 to∏
     
  4. Apr 1, 2013 #3
    Haha! I just realized my mistake as soon as you posted! Thank you very much!

    To be clear for anyone who looks at this post for help in the future,

    Ex = (Kλ/R)*∫3/2ππ/2(cosθ)dθ

    Since the integral from pi/2 to 3pi/2 is not going to have the correct coordinates to give you the correct length, you must integrate from 0 to pi since the shape is a semicircle (half a circle) or from 0 to pi on a trigonometric circle.

    When you integrate from 0 to pi/2, the charge for half the semicircle is 240072.2588752749

    Multiply that number by two, and the correct answer is:

    4.9×105 N/C


    Thanks again!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted